President Barack Obama’s health care reform law will be center stage again this week, as Republicans look to put coordinated bicameral pressure on Senate Democrats to take up a full repeal of the controversial law.

House Republicans pledged for months to offer a full repeal if the law was upheld by the Supreme Court, and on Wednesday they will do just that when they vote on a measure sponsored by Majority Leader Eric Cantor (R-Va.).

“The House passed a similar bill last year, but it died in the Democratic-controlled Senate,” Speaker John Boehner (R-Ohio) wrote in a Friday op-ed in the Washington Times. “By passing our repeal bill in July, we will give the Senate and Mr. Obama a second opportunity to follow the will of the American people.”

Senate Democrats, meanwhile, will pivot to jobs and the economy, contending that the Supreme Court’s decision to uphold the health care law should put the issue to rest. But Senate Republicans do not appear willing to acquiesce.

In his own Friday opinion piece in the Times, Minority Leader Mitch McConnell reiterated plans to push Senate Democrats — especially those up for re-election — to vote to repeal the law. McConnell and other Republicans have seized on the court ruling’s declaration that the law’s mandate to buy health insurance is constitutional because it acts as a tax on those who decline.

“It’s time for Democrats to stop defending the indefensible and to join us in repealing this colossal mistake. The court’s decision gives us the clearest proof yet that this law has to go, so we can clear the way for common-sense, step-by-step reforms that protect Americans’ access to the care they need, from the doctor they choose, at a lower cost,” the Kentucky Republican wrote.

Unlike in the House, where Republicans can schedule repeal votes at will, Senate Republicans will have to use procedural maneuvering or amendments to work the issue onto the Senate’s agenda, which is dictated by Majority Leader Harry Reid. The Nevada Democrat has scheduled a test vote for Tuesday on a package of tax breaks designed to promote hiring and new equipment purchases by small businesses.

Senior Democratic aides indicated Friday that Republicans are not expected to block the measure from coming up, but they are concerned that GOP Senators will try to use the bill as a vehicle for their own agenda.

Republicans could offer amendments on repeal of the health care law or its tax components, or an extension of the tax cuts implemented under President George W. Bush.

Much like McConnell, House Ways and Means Chairman Dave Camp will dig in on Chief Justice John Roberts’ ruling with a Tuesday hearing examining the tax ramifications of the health care law.

“I strongly disagree with the Court’s decision and its holding that Congress can tax Americans who choose not to purchase government-approved health insurance,” the Michigan Republican said in a statement last week. “This ruling sets a dangerous precedent with potentially enormous consequences.”

The committee is still working on a nonbinding measure that would lay out the majority’s markers for tax reform, and the House will likely vote on that measure along with an extension of the Bush-era tax cuts during the last week of July, just before the House breaks for August recess.

In the Senate, Reid may also bring up this month a bill designed to curb outsourcing of jobs by giving tax breaks to companies bringing jobs back to the U.S., a senior Democratic aide said. The bill would also eliminate current tax breaks for companies that send jobs overseas. The measure — a feature of Obama’s to-do list — lines up with a Democratic attack on presumptive GOP presidential nominee Mitt Romney. However, similar bills championed by former Sen. Byron Dorgan (D-N.D.) failed to gain traction in the past.

Still, even if the measures pass the Senate, the House is unlikely to take up Obama’s priority legislation. Instead, a House leadership aide said the middle of the month will be dedicated to Defense appropriations measures and to an attempt to roll back the automatic defense sequester that was triggered by the failure last year of the super committee to draft a deficit reduction package. Votes will also be held on a spate of bills designed to reduce government regulations, which Republicans say are hampering job growth.

One measure that may not reach the House floor is a farm bill. The Senate has already passed its version, and last week, House Agriculture Committee leaders released a bill that would save $35.1 billion over 10 years, with much of the cuts coming from the Supplemental Nutrition Assistance Program, also known as food stamps.

But the bill may not go far amid tepid interest from GOP leaders in picking a fight with their conservative base. Conservatives have targeted the SNAP program and intend to offer more cuts in committee. The bill will be marked up on Wednesday.

“There will be challenges ahead, but we will pass the bill out of Committee ... and, if the House leadership gets this right and brings the bill to the floor, we will ultimately finish the bill in September,” Agriculture ranking member Collin Peterson (D-Minn.) said in a statement last week.